Figure 14: The lag time in the auxiliary reaction mechanism (47)–(48) when t_s2 ≪ t_c1 ≪ t_c2 ≪ t_s1.

The thick black curve is the numerically-integrated solution to the mass action equations (49a)–(49d), and the unfilled circles mark the inner solution given by (103). The leftmost dashed vertical line corresponds to t_c2, and the rightmost dashed vertical line corresponds to $t_{c_2}^{\ast }=-t_{c_2}\text{ln}{t}_{c_2}∕t_{s_1}$. The lower dotted horizontal line corresponds to y = ℓ; The constants (without units) used in the numerical simulation are: $e_1^0=1$, $s_1^0=1000$, $e_2^0=1$, k₁ = 1, k₂ = 1, k₃ = 1, k₋₃ = 1, k₄ = 100 and k₋₁ = 1. Time has been mapped to the t_∞ scale: t_∞(t) = 1 – 1/ln[t + exp(1)], and c₂ has been numerically-scaled by its maximum value.